Báo cáo khoa học: " Spatial variability of humus forms in some coastal forest ecosystems of British Columbia" pdf

Original
article
Spatial
variability
of
humus
forms
in
some
coastal
forest
ecosystems
of
British
Columbia
H Qian,
K
Klinka
Forest
Sciences
Department,
University
of
British
Columbia,
Vancouver,
BC,
Canada
V6T
1Z4
(Received

1
February
1994;
accepted
19
June
1995)
Summary —
The
spatial
variability
of
5
humus
form
properties
(thickness,
acidity,
total
C,
total
N and
mineralizable-N)
was
examined
in
3
coastal
forest
sites

of
different
tree
species
composition
(western
hemlock,
Douglas-fir
and
western
redcedar),
humus
forms,
and
ecological
site
quality
using
variogram
and
kriging.
Humus
form
properties
were
found
spatially
dependent
and
the

kriging
interpolation
between
sample
locations
unbiased
for
all
5
properties
and
in
all
3
sites.
The
overall
range
of
spatial
dependence
ranged
from
46
to
1
251
cm,
but
varied

with
property
and
site.
The
average
range
for
the
humus
form
properties
increased
from
109
cm
(total
N)
to
704
cm
(mineralizable-N),
and
that
for
the
sites
increased
from
275

cm
(western
hemlock)
to
581
cm
(Douglas-fir).
It
appears
that
humus
forms
in
each
site
occur
in
polygons
with
the
lateral
dimension
ranging
from
100
to
700
cm.
The
spatial

pat-
tern
of
each
property
in
each
site
was
portrayed
in
contour
maps.
humus
form
/
spatial
variability
/
variogram
/
kriging
Résumé —
Variabilité
spatiale
des
types
d’humus
dans
quelques

écosystèmes
forestiers
côtiers
de
Colombie
britannique.
La
variabilité
spatiale
de
5
caractéristiques
de
l’humus
(épaisseur,
aci-
dité,
carbone
total,
azote
total
et
minéralisable)
a
été
étudiée
dans
3
sites
forestiers

côtiers,
différant
par
l’espèce
dominante
(pruche
de
l’Ouest,
douglas
et
thuya
géant),
le
type
d’humus
et
le
type
de
station.
Elle
est
analysée
par
variogramme
et
krigeage.
Ces
propriétés
des

types
d’humus
sont
dépen-
dantes
spatialement,
et
l’interpolation
par
krigeage
entre
les
points
d’échantillonnage
est
non
biaisée
pour
les
5
propriétés
et
les
3
sites.
La
portée
globale
de
dépendance

spatiale
varie
de
46
à
1 251
cm,
mais
dépend
de
la
propriété
considérée
et
du
site.
La
portée
moyenne
pour
les
propriétés
de
l’humus
varie
entre
109
cm
(pour
l’azote

total)
à
704
cm
(pour
l’azote
minéralisable),
et
cella
des
sites
varie
entre
275
cm
(sous
pruche
de
l’Ouest)
à
581
cm
(sous
douglas).
Il
apparaît
que
les
types
d’hu-

mus
dans
chaque
site
sont
groupés
en
polygones
dont
la
dimension
varie
entre
100
et
700
cm.
La
varia-
bilité
spatiale
de
chaque
propriété
dans
chaque
site
est
illustrée
par

des
cartes
obtenues
par
kri-
geage.
type
d’humus
/ variabilité
spatiale
/ variogramme
/
krigeage
INTRODUCTION
Humus
form
is
a
group
of
soil
horizons
located
at
or
near
the
surface
of
a

pedon,
which
have
formed
from
organic
residues,
either
separate
from,
or
intermixed
with,
mineral
materials
(Green
et al,
1993).
In
consequence,
humus
forms
may
be
com-
prised
of
entirely
organic
or

both
organic
and
mineral
(melanized
A)
horizons.
Due
to
the
difficulties
in
combining
organic
and
mineral
horizons
in
chemical
and
data
anal-
yses
(Lowe
and
Klinka,
1981),
this
study
examined

only
the
organic
or
the
forest
floor
portion
of
humus
forms.
As
the
product
of
biologically
mediated
decomposition
processes,
the
humus
form
that
has
developed
on
a
particular
site
depends

on
the
biota
and
environment
of
that
site.
Both
biota
and
environment
may
change
over
a
short
distance,
yielding
a
variety
of
microsites
which
support
the
development
of
different
humus

forms.
The
nature
of
spatial
variability
in
humus
forms
is
itself
scale-dependent
because
the
factors
and
processes
of
humus
formation
interact
over
many
different
spatial
scales.
It
seems
reasonable
to

assume
that,
on
average,
the
closer
humus
forms
are
to
each
other,
whether
in
space
or
time,
the
more
likely
it
is
their
properties
will
be
similar.
This
assump-
tion

calls
for
an
inquiry
into
the
nature
and
degree
of
spatial
dependence
between
the
humus
forms,
particularly
in
the
sample
plots
chosen
to
represent
individual
ecosystems,
ie
segments
of
landscape

relatively
uniform
in
climate,
soil
and
vegetation
(Pojar
et
al,
1987).
Classical
statistical
techniques
are
unable
to treat
adequately
the
spatial
aspect
of
data
in
which
neighboring
samples
may
not
be

independent
of
each
other;
furthermore,
they
do
not
consistently
provide
unbiased
estimates
for
unsampled
points,
or
estimate
optimal
variances
for
the
interpolated
val-
ues
(Matheron,
1963;
Journel
and
Hui-
jbregts,

1978;
Yost
et al,
1982a;
Robertson,
1987;
Rossi
et al,
1992).
Geostatistics can
be
used
to
quantify
the
spatial
dependence
between
sampling
locations
and
to
provide
optimal
estimates
for
unsampled
locations
(Matheron,
1963, 1971;

Burgess
and
Web-
ster,
1980a;
Vieira
et al,
1981;
Yost
et al,
1982b).
Central
to
geostatistics
is
the
vari-
ogram,
which
models
the
average
degree
of
similarity
between
the
values
as
a

function
of
their
separation
distance,
and
kriging,
which
estimates
values
for
unsampled
loca-
tions
without
bias
and
with
minimum
vari-
ance.
Geostatistics
has
been
extensively
used
in
mining
(eg Matheron,
1963, 1971;

Krige,
1966;
David,
1977;
Clark,
1979;
Journel
and
Huijbregts,
1978)
and,
more
recently
applied
in
soil
science
(eg Nielsen
et al,
1973;
Big-
gar
and
Nielsen,1976;
Campbell,
1978;
Burgess
and
Webster,
1980a,

b;
Vieira
et
al,
1981;
Yost
et al,
1982a,
b;
Xu
and
Web-
ster,
1984),
hydrology
(eg McCullagh,
1975;
Delhomme,
1976, 1978,
1979;
Hajrasuliha
et al,
1980;
Kitandis,
1983),
ecology
(eg
Robertson,
1987;
Kemp

et al,
1989),
veg-
etation
science
(eg Palmer,
1988;
Fortin
et
al,
1989),
but
no
systematic
effort
has
yet
been
made
to
apply
it
to
humus
form
stud-
ies.
The
objective
of

this
study
was
to
exam-
ine
the
spatial
variation
of
5
selected
humus
form
properties -
thickness,
acidity,
total
C,
total
N and
mineralizable-N -
in
disturbed
and
undisturbed
coastal
forest
ecosystems.
This

objective
was
accomplished
by
employ-
ing
variogram
and
kriging
for
the
analysis
of
spatial
variability
of
these
properties.
The
thickness
was
thought
the
most
variable
morphological
property,
reflecting
difference
in

the
deposition
and
decomposition
of
organic
residues
in
both
space
and
time.
The
significance
of
the
4
selected
chemical
properties
has
been
long
recognized
in
humus
form
classification
(Green
et al,

1993).
MATERIALS
AND
METHODS
All
study
sites
were
located
near
Vancouver,
British
Columbia,
and
were
within
the
Coastal
Western
Hemlock
(CWH)
zone,
which
delineates
the
sphere
of
influence
a
cool

mesothermal
cli-
mate
(Klinka
et al,
1991).
The
soils
in
the
area
are
typically
coarse-textured
humo-ferric
podzols
(Canada
Soil
Survey
Committee,
1978)
derived
from
granitic
morainal
deposits.
The
study
sites
were

deliberately
chosen
to
represent
forest
ecosystems
with
different
veg-
etation,
humus
forms,
ecological
site
quality
and
history
of
disturbance
(table
I).
The
first
site
(Hw)
was
dominated
by
western
hemlock

(Tsuga
het-
erophylla
[Raf]
Sarg),
the
second
(Fd)
by
Dou-
glas-fir
(Pseudotsuga
menziesii
[Mirbel]
Franco),
and
the
third
(Cw)
by
western
redcedar
(Thuja
plicata
Donn
ex
D
Don).
The
western

hemlock
site
had
a
well-developed
moss
layer
dominated
by
Plagiothecium
undulatum
(Hedw)
BSG,
and
Mors
(Hemimors
and
Lignomors)
(Green
et
al,
1993)
were
the
prevailing
humus
forms;
the
Dou-
glas-fir

site
had
a
well-developed
herb
layer
with
abundant
Polystichum
munitum
(Kaulf)
Presl
and
Dryopteris
expansa
(K
Presl)
Fraser-Jenkins
&
Jermy,
and
Mormoders
were
the
prevailing
humus
forms;
and
the
western

redcedar
site
had
well-
developed
shrub
and
herb
layers
dominated
by
Athyrium
filix-femina
(L)
Roth,
Rubus
spectabilis
Pursh
and
Tiarella
trifoliata
L,
and
Leptomoders
and
Mullmoders
were
the
prevailing
humus

forms
(table
III).
Using
the
methods
described
by
Klinka
et
al
(1984,
1989),
the
western
hemlock
site
was
considered
slightly
dry
and
nitrogen-poor;
the
Douglas-fir
site,
fresh
and
nitrogen-rich
and

the
western
redcedar
site,
moist
and
nitrogen-very
rich.
At
each
study
site,
a
20
x
20
m
(0.04
ha)
sam-
ple
plot
was
located
to
represent
an
individual
ecosystem.
Within

each
plot,
a
10
x
10
grid,
1
x
1
m,
and
a
7
x
7
grid,
15
x
15
cm,
were
laid
out
for
sampling
humus
forms.
One-hundred
discontin-

uous
samples
were
collected
from
the
large,
10
x
10
grid
at
the
center
of
each
1
x
1
m
quadrant,
and
49
contiguous
samples
were
taken
from
the
small,

7 x
7 grid -
a
total
of
149
humus
form
sam-
ples
per
site.
The
small
grid
provided
data
for
the
analysis
of
a
small-scale
pattern
(the
sampling
interval
of
15
cm),

while
the
large
grid
provided
data
for
the
analysis
of
a
large-scale
pattern
(the
sampling
interval
of
1
m).
Each
humus
form
sample
was
a
composite
of
all
of
its

organic
horizons
(except
recently
shed
lit-
ter),
and
represented
a
uniform,
15
x
15
cm
col-
umn
cut
by
knife
from
the
ground
surface
to
the
boundary
with
mineral
soil.

Each
sample
was
described
and
identified
according
to
Green
et
al (1993),
its
grid
location
recorded
and
its
thick-
ness
determined
by
taking
4
measurements
at
each
cardinal
direction
with
a

steel
ruler.
All
samples
were
air-dried
to
constant
mass
and
ground
in
a
Wiley
mill
to
pass
through
a
2-mm
sieve.
The
chemical
analysis
was
done
by
Pacific
Soil
Analysis

Inc
(Vancouver,
BC)
and
the
results
were
expressed
per
unit
of
mass
(tables
II
and
III).
Humus
form
pH
was
measured
with
a
pH
meter
and
glass
electrode
in
water

using
a
1:5
suspension.
Total
C
(tC)
was
determined
using
a
Leco
Induction
Furnace
(Bremner
and
Tabatabai,
1971).
Total
N
(tN)
was
determined
by
semimicro-
kjeldahl
digestion
followed
by
determination

of
NH
4
-N
using
a
Technicon
Autoanalyzer
(Anony-
mous,
1976).
Mineralizable-N
(min-N)
was
deter-
mined
by
an
anaerobic
incubation
procedure
of
Powers
(1980)
with
released
NH
4
determined
colorimetrically

using
a
Technicon
Analyzer.
For
the
geostatistical
analyses,
we
used
the
GS
+
geostatistical
package
(Gamma
Design
Soft-
ware,
1992)
following
the
theory
and
principles
given
by
Matheron
(1963,
1971),

Journel
and
Huijbregts
(1978),
David
(1977),
Delhomme
(1978),
Vieira
et al (1981,
1983),
Vauclin
et al
(1983),
Webster
(1985),
Trangmar
et al (1985)
and
lsaaks
and
Srivastava
(1989).
Consider
that
a
humus
form
property
is

a
regionalized
variable
Z(x)
and
that
its
measurements
at
places
xi,
i
= 1,
2, 3,
,
n,
constitute
n
discrete
points
in
space,
where
xi
denotes
a
set
of
spatial
coordinates

in
2
dimensions.
The
measurements
give
a
set
of val-
ues
z(x
i
),
and
the
semivariance
that
summarizes
the
spatial
variation
for
all
possible
pairing
of
data
is
calculated
by:

where
the
value
&jadnr;(h)
is
the
estimated
half-
or
semivariance
for
h,
which
is
a
vector
known
as
the
lag,
with
both
distance
and
direction,
and
N(h)
is
the
number

of
pairs
of
points
separated
by
h.
A
plot
of
the
estimated
&jadnr;((h)
values
against
h
is
called
a
semivariogram
or
variogram.
By
definition,
the
variogram
value
at
zero
lag

should
be
zero,
but
in
practice
it
usually
inter-
cepts
the ordinate
at
a
positive
value
known
as
the
nugget
variance
(c
0
).
The
nugget
represents
mea-
surement
error
and

unexplained
or
random
spa-
tial
variability
at
distances
smaller
than
the
small-
est
sampling
interval.
The
variogram
value
at
which
the
plotted
points
level
off
is
known
as
the
sill,

which
is
the
sum
of
nugget
variance
(c
0)
and
structural
variance
(c),
and
the
lag
distance
(a)
at
which
the
variogram
levels
off
is
known
as
the
range
(or

the
zone
of
influence)
beyond
which
there
is
no
longer
spatial
correlation
and,
hence,
no
longer
spatial
dependence.
Local
estimation
by
kriging
required
fitting
a
continuous
function
to
the
computed

experimen-
tal
semivariance
values.
The
most
commonly
used
models
are:
linear,
linear
with
sill,
spheri-
cal,
exponential
and
gaussian
(Journel
and
Hui-
jbregts,
1978;
Tabor
et
al,
1984;
McBratney
and

Webster,
1986;
Oliver
and
Webster,
1986).
Exper-
imental
variogram
values
for
each
humus
form
property
were
fitted
to
each
model
by
least
square
approximation.
Using
Akaike’s
(1973)
informa-
tion
criterion

(AIC),
the
spherical
(eq
[2])
and
exponential
(eq
[3])
isotropic
models
were
found
best
fitting
the
data:
where
c0,
c,
a
and
a0
are
nugget
variance,
struc-
tural
variance,
range

and
range
parameter,
respectively.
Because
the
semivariance
from
an
exponential
isotropic
model
approaches
the
sill
asymptotically,
there
is
no
absolute
range.
A
work-
ing
range
of
a
=
3
a0,

a
lag
at
which
the
semi-
variance
is
95%
of
the
sill
values,
was
estimated
for
practical
purposes
(Oliver
and
Webster,
1986).
With
appropriate
variogram
models
defined,
kriging
was
used

to
interpolate
between
sample
points
and
to
estimate
the
values
for
unsampled
locations.
Kriging
is
a
weighted
moving
average
with
an
estimator:
where
n
is
the
number
of
values
z(x

i)
for
the
sam-
pled
locations
involved
in
the
estimation
of
the
unsampled
location
x0,
and
λ
i
are
the
weights
associated
with
each
sampled
location
value.
Kriging
is
considered

an
optimal
estimation
method
as
it
estimates values
for
unsampled
locations
without
bias
and
with
minimum
vari-
ance.
No
estimation
method
is
without
estima-
tion
errors,
thus
there
is
an
error

associated
with
kriging.
The
magnitude
of
this
error
will
be
a
mea-
sure
of
the
validity
of
estimation.
The
goodness
of
estimation
can
be
determined
by
comparing
the
difference
between

the
measured
value
at
a
given
location
with
its
kriged
value
at
the
same
loca-
tion,
using
neighborhood
values
but
not
the
mea-
sured
value
itself.
Thus,
if
for
each

location
with
a
measured
value
z(x
i
),
where
i =
1,
2,
3, ,
n,
the
estimated
value
is
&jadnr;(x
i
),
where
i=
1,
2, 3,
,
n,
then
the
calculated

set
of
estimated
errors
is
ϵ
i
=
&jadnr;(x
i
) -
&jadnr;(x
i
),
where
i
=
1, 2, 3,
,
n.
The
good-
ness
of
estimation
is
expressed
by
2
conditions

on
the
estimated
error:
1)
a
mean
error,
me,
close
to
zero -
this
property
of
the
estimator
is
known
as
unbiasedness,
and
2)
dispersion
of
the
errors
was
to
be

concentrated
around
m
ϵ
-
this
being
expressed
by
a
small
value
of
the
estimated
vari-
ance
σϵ
2
(table
VI).
For
statistical
analyses,
we
used
the
SYSTAT
(Wilkinson,
1990a,

b).
Prior
to
geostatistical
anal-
ysis,
humus
form
variables
for
each
study
stand
were
examined
for
normality,
using
probability
distribution
diagrams
(Wilkinson,
1990a).
The
thickness
values
in
the
western
hemlock

and
Douglas-fir
sites
and
the
acidity
and
min-N
values
in
the
Douglas-fir
site
were
log-transformed
as
they
were
found
log-normally
distributed.
RESULTS
AND
DISCUSSION
A
univariate
summary
of
humus
form

data
according
to
study
sites
suggested
the
pres-
ence
of
comparable
mean
values
for
the
5
properties
but
dissimilar
distributions,
except
for
mineralizable-N
(table
II).
The
values
of
coefficient
of

variation
and
variance
implied
trends
of
a
low
variability
around
mean
acid-
ity
and
total
C
(except
in
the
western
red-
cedar
site),
a
moderate
variability
around
mean
total
N

and
a
high
variability
around
mean
thickness
and
mineralizable-N.
Skew-
ness
values
indicated
an
asymmetric
dis-
tribution
for
each
property
in
1
or
2
study
sites
(table
II).
When
considering

the
skew-
ness
values
(table
II)
and
the
univariate
summary
of
data
stratified
according
to
both
humus
form
taxa
and
study
sites
(table
III),
the
acidity
data
for
the
Douglas-fir

site
were
strongly
skewed
to
the
right,
reflecting
the
presence
of
relatively
less-acid
Leptomod-
ers
occupying
mineral
mounds.
The
acidity
and
carbon
data
for
the
western
redcedar
site
were
skewed

to
the
right
and
left,
respectively,
attesting
to
the
presence
of
more-acid
and
carbon-richer
Lignomoders
relative
to
dominant
Leptomoders.
The
total
N
data
for
both
Douglas-fir
and
western
hemlock
sites

were
strongly
skewed
to
the
left,
indicating
the
presence
of
nitrogen-
richer
Mormoders
relative
to
the
other
humus
forms
on
these
sites.
In
the
Dou-
glas-fir
site,
the
distribution
of

mineralizable-
N
was
skewed
to
the
right,
manifesting
the
presence
of
Lignomors -
the
humus
form
with
the
lowest
concentration
of
available
N.
The
distribution
of
thickness
data
in
both
Douglas-fir

and
western
hemlock
sites
was
highly
asymmetric
and
strongly
skewed
to
the
right,
indicating
the
presence
of
dis-
turbed
microsites
(mineral
mounds)
with
thin
forest
floors.
Although
univariate
measures
provided

useful
summaries,
they
did
not
describe
spatial
continuity
of
the
data,
ie
the
rela-
tionship
between
the
value
for
a
property
in
one
location
and
the
values
for
the
same

property
at
another
’location.
The
spatial
continuity
of
each
humus
form
property
and
study
site
was
examined
by
the
variograms
computed
as
an
average
overall
direction
using
equation
[1
] and

assuming
isotropy -
similar
spatial
continuity
with
direction.
The
data
collected
from
the
small,
7 x
7 grids
were
used
for
the
lag
distance
(h)
≤ 100
cm,
and
those
collected
from
the
large

10 x 10
grid
were
used
for
the
lag
distance
>
100
cm.
Although
the
maximum
lag
dis-
tance
could
have
been
1
000
cm,
the
max-
imum
h of
800
cm
was

used
in
order
to
have
each
lag
class
adequately
represented
by
a
sufficient
number
of
data.
The
parameters
of
the
models
fitted
to
experimental
variograms
are
given
in
table
IV,

and
the
fitted
regression
lines
are
shown
in
figure
1.
The
models
used
for
fitting
pro-
duced
transitive
variograms,
which
are
forms
of
second-order
stationarity
with
finite
vari-
ances
represented

by
the
sill;
the
spherical
models
represent
the
variograms
with
fixed
range,
the
exponential
models
the
vari-
ograms
without
fixed
range.
The
computed
and
plotted
variograms
showed
that
the
distribution

of
each
of
the
5
humus
properties
is
not
random
but
spa-
tially-dependent
as
their
estimated
vari-
ogram
values
increase
with
increasing
lags
to
their
sills,
at
a
finite
lag

or
approaching
the
sill
asymptotically
(table
IV,
fig
1).
Over-
all,
the
variograms
were
generically
similar,
reflecting
relatively
small
differences
in
spa-
tial
continuity
of
their
properties,
and
imply-
ing

a
small-scale
spatial
pattern
of
humus
form
variability.
Despite
the
overall
similar-
ity,
the
variograms
varied
with
property
and
site.This
suggested
that
each
property
has
a
somewhat
different
spatial
pattern

imposed
by
the
property
itself,
the
factors
controlling
humus
form
development
in
each
site,
and
the
history
of
site
disturbance.
The
average
range
values
for
the
humus
form
properties
increased

from
109
cm
for
total
N
to
708
cm
for
mineralizable-N,
and
those
for
the
study
sites
increased
from
275
cm
in
the
western
hemlock
site
to
581
cm
in

the
Douglas-fir
site.
Thus,
the
ranges
beyond
which
humus
forms
are
no
longer
spatially
dependant
were
short
for
both
the
properties
and
sites.
It
appears
that
in
all
study
sites

humus
forms
have
developed
in
polygons
with
the
lateral
dimension
rang-
ing
from
about
100
to
700
cm,
and
that
their
spatial
continuity
increases
somewhat
from
disturbed
to
undisturbed
sites.

The
property
with
the
absolutely
short-
est
range
(46
cm)
was
total
N
in
the
dis-
turbed
western
hemlock
site
(table
IV,
fig
1).
This
feature
manifests
a
nearly
random

spatial
pattern
of
Hemimors
and
Mormoders
versus
Lignomors
and
Lignomoders,
each
pair
with
strongly
contrasting
N
concentra-
tions
(table
III).
The
property
with
the
abso-
lutely
longest
range
(1
251

cm)
was
miner-
alizable-N
in
the
Douglas-fir
site
(table
IV).
This
feature
indicates
a
low
spatial
variabil-
ity,
which
might
be
related
to
a
uniform
for-
est
floor
cover
resulting

from
disturbance.
To
compare
the
nugget
effect
within-
and
between-site,
relative
nugget
variances,
ie
(real)
nugget
variances
out
of
sills
in
per-
centage,
were
calculated
(table
IV).
These
variances
also

varied
with
property
and
site
(fig
1).
The
relative
nuggets
for
easily
mea-
sured
thickness
and
acidity
were
clearly
smaller
than
those
for
total
C,
total
N and
mineralizable-N
(table
IV),

ie the
properties
with
a
greater
likelihood
of
analytical
error.
The
low
relative
nuggets
for
thickness
and
acidity,
ranging
from
0.2
to
14.0%,
indicated
that
their
structural
variances
account
for
more

than
85%
of
their
sill
variances
and
approach
their
overall
sample
variances.
The
high
relative
nuggets
for
total
C,
total
N and
mineralizable-N,
ranging
from
32
to
70%,
indicated
that
their

nuggets
represent
a
large
proportion
of
their
total
variance
that
can
be
modelled
as
spatial
dependence
from
the
available
sampling
scheme.
Using
the
variogram
models
(table
IV)
with
kriging
algorithm

(eq
[4]),
the
values
for
each
of
the
5
humus
form
properties
were
estimated
for
a
total
of
1
581
unsam-
pled
locations
in
each
large
(10
x
10 m)
grid.

Since
the
configuration
of
sampling
loca-
tions
had
the
regular,
100
cm
sampling
inter-
val
and
the
interval
for
kriging
was
25
cm,
each
of
the
1
681

measured-plus-kriged
points
was
located
at
the
nodes
of
the
25
x
25
cm
grid.
Each
kriged
point
was
estimated
using
16
measured
points
around
it.
The
means
and
standard
deviations

for
the
mea-
sured
values
(n
= 100)
and
the
measured-
plus-kriged
values
(n
=
1
681)
are
given
in
table
V.
The
mean
estimated
errors
were
sub-
mitted
to
t-test

(Zar,
1984;
table
VI).
Com-
pared
to
the
value
of
1.984
for
t
0.05
(2),
99
,
all
the
mean
estimated
errors
were
signifi-
cantly
equal
to
zero,
except
for

mineraliz-
able-N
in
the
Douglas-fir
site
with
mean
esti-
mated
error
close
to
1.984.
The
verification
of
the
low
variance
also
showed
that
the
percentages
of
the
observed
estimation
errors

were
within
m
ϵ

±
2σ
ϵ
,
except
a
few
cases
where
the
errors
were
slightly
smaller
than
95%.
As
a
supplement
to
the
spatial
analysis,
the
contour

maps
based
on
the
measured-
plus-kriged
values
were
produced
for
each
of
the
5
humus
form
properties
in
each
of
the
3
10
x
10 m
study
sites
(fig
2).
We

con-
sider
these
maps
more
precise
(with
the
precision
definable
in
terms
of
the
kriging
variance)
than
those
which
would
be
pro-
duced
from
the
original
samples,
as
16.81
times

more
values
were
used
to
construe
a
picture
of
spatial
continuity.
The
maps
illustrate
the
interpretations
made
earlier
from
variograms,
ie
the
distribution
of
all
5
humus
form
properties
is

spatially-depen-
dent
and
generically
similar,
and
that
the
5
humus
form
properties
measured
in
the
3
study
sites
are
spatially
continuous
over
a
short
distance.
Furthermore,
the
maps
illus-
trate

an
aspect
which
was
not
examined
in
this
study -
a
joint
spatial
dependence
between
humus
form
properties.
For
exam-
ple,
the
right
center
and
lower
right
regions
of
the
10

x
10 m
grid
for
the
Douglas-fir
site
(fig
2,
center)
shows
relatively
thicker
humus
forms.
Relative
to
other
regions
of
the
grid,
the
same
area
is
also
shown
to
have

a
higher
acidity,
higher
total
C
concentration
and
lower
total
N and
mineralizable-N
con-
centrations,
ie
the
characteristics
of
Lig-
nomors
and
Lignomoders,
which,
in
fact,
were
the
prevailing
humus
forms

in
these
2
regions.
CONCLUSION
The
spatial
analysis
of
5
humus
form
prop-
erties
in
3
sites
showed
the
presence
of
a
distinct
pattern
that
reflected
spatial
depen-
dence.
The

structural
spatial
dependence
ranged
from
46
to
1
251
cm,
and
varied
somewhat
with
property
and
site.
The
most
spatially
continuous
property
was
mineral-
izable-N,
and
the
most
spatially
discontinu-

ous
property
was
total
N.
The
results
sug-
gest
a
relatively
low
spatial
continuity
and
small-scale
pattern
of
humus
form
devel-
opment
which
appears
to
occur
in
polygons
with
the

lateral
dimension
ranging
from
about
100
to
700
cm.
ACKNOWLEDGMENTS
We
thank
Dr
H
Schreier,
Department
of
Soil
Sci-
ence,
University
of
British
Columbia,
Dr
A
Franc,
Département
de

Mathématiques
Appliquées
et
Informatique,
ENGREF,
and
one
anonymous
reviewer
for
helpful
comments
on
the
manuscript.
Financial
support
for
this
study
was
provided,
in
part,
by
the
Natural
Science
and
Engineering

Council
of
Canada.
REFERENCES
Akaike
H
(1973)
Information
theory
and
an
extension
of
maximum
likelihood
principle.
In:
Second
Inter-
national
Symposium
on
Information
Theory
(BN
Petrov,
F
Csáki,
eds),
Akadémia

Kiadó,
Budapest,
267-281
Anonymous
(1976)
Technicon
autoanalyzer.
II.
Method-
ology:
industrial
individual/simultaneous
determina-
tion
of
nitrogen
and/or
phosphorus
in
BD
acid
digest.
Industrial
Method
329/4W/A,
Technicon
Corpora-
tion.
Tarrytown,
New

York,
USA
Biggar
JW,
Nielsen
DR
(1976)
Spatial
variability
of
the
leaching
characteristics
of
a
field
soil.
Water
Resour
Res
12,
78-84
Bremner
JM,
Tabatabai
MA
(1971)
Use
of
automated

combustion
techniques
for
total
carbon,
total
nitrogen,
and
total
sulphur
analysis
of
soils.
In:
Instrumental
methods
for
analysis
of
soils
and
plant
tissue
(LM
Walsh,
ed),
Soil
Science
Society
of

America,
Madi-
son,
WI,
USA,
1-16
Burgess
TM,
Webster
R
(1980a)
Optimal
interpolation
and
isarithmic
mapping
of
soil
properties.
I.
The
semi-
variogram
and
punctual
kriging.
J
Soil
Sci
31,

315-
331
Burgess
TM,
Webster
R
(1980b) Optimal
interpolation
and
isarithmic
mapping
of
soil
properties.
II.
Block
kriging.
J
Soil
Sci 31,
333-341
Campbell
JB
(1978)
Spatial
variation
of
sand
content
and

pH
within
single
contiguous
delineations
of
2
soil
mapping
units.
Soil
Sci
Soc Amer J 42,
460-464
Canada
Soil
Survey
Committee
(1978)
The
Canadian
system
of
soil
classification.
Publ
1646,
Can
Dept
Agric,

Ottawa,
Ontario
Clark
I (1979)
Practical
geostatistics.
Applied
Science
Publishers,
London,
UK
David
M
(1977)
Geostatistical
ore
reserve
estimation.
Elsevier,
Amsterdam
Delhomme
JP
(1976)
Kriging
in
hydrosciences.
Centre
d’informatique
géologique,
Fontainebleau,

France
Delhomme
JP
(1978)
Kriging
in
the
hydrosciences.
Adv
Water
Resour
1,
251-266
Delhomme
JP
(1979)
Spatial
variability
and
uncertainty
in
groundwater
flow
parameters:
a
geostatistical
approach.
Water
Resour
Res

15,
269-280
Fortin
MJ,
Drapeau
P,
Legendre
P
(1989)
Spatial
auto-
correlation
and
sampling
design
in
plant
ecology.
Vegetatio
83,
209-222
Gamma
Design
Software
(1992)
GS
+:
professional
geo-
statistics

for the
PC.
Version
2.
Plainwell,
MI,
USA
Green
RN,
Trowbridge
RL,
Klinka
K
(1993)
Toward
a
taxonomic
classification
of
humus
forms.
For
Sci
Monogr 29, 1-48
Hajrasuliha
S,
Baniabbassi
N,
Metthey
J,

Nielsen
DR
(1980)
Spatial
variability
of
soil
sampling
for
salinity
studies
in
south-west
Iran.
Irrigation
Science
1, 197-
208
Isaaks
EH,
Srivastava
RM
(1989)
Spatial
continuity
mea-
sures
for
probabilistic
and

deterministic
geostatis-
tics.
Math
Geol 20,
313-341
Journel
AG,
Huijbregts
CJ
(1978)
Mining
geostatistics.
Academic
Press,
London,
UK
Kemp
WP,
Kalaris
TM,
Quimby
WF
(1989)
Rangeland
grasshopper
(Orthoptera:
Acrididae)
spatial
vari-

ability:
macroscale
population
assessment.
J
Econ
Entom 82, 1270-1276
Kitandis
DK
(1983)
Statistical
estimation
of
polynomial
generalized
covariance
functions
and
hydrological
applications.
Water
Resour
Res
19,
909-921
Klinka
K,
Green
RN,
Courtin

PJ,
Nuzsdorfer
FC
(1984)
Site
diagnosis
tree
species
selection,
and
slashburn-
ing
guidelines
for
the
Vancouver
Forest
Region.
BC
Min
For,
Land
Manage
Rep
no
8,
Victoria,
BC,
Canada
Klinka

K,
Krajina
VJ,
Ceska
A,
Scagel
AM
(1989)
Indi-
catorplants
of coastal British
Columbia.
University
of
British
Columbia
Press,
Vancouver,
BC,
Canada
Klinka
K,
Pojar J,
Meidinger
DV
(1991)
Revision
of
bio-
geoclimatic

units
of
coastal
British
Columbia.
North-
west Sci
65, 32-47
Krige
DG
(1966)
Two-dimensional
weighted
moving
average
trend
surfaces
for
ore
evaluation.
In:
Proc
Symp
on
Mathematics,
Statistics,
and
Computer
Applications
in

Ore
Evaluation.
South
African
Institute
of
Mining
and
Metallurgy,
Johannesburg
Lowe
LE,
Klinka
K
(1981)
Forest
humus in
the
Coastal
Western
Hemlock
biogeoclimatic
zone
of
British
Columbia
in
relation
to
forest

productivity
and
pedo-
genesis.
BC
Min
For,
Res
Note
no
89,
Victoria,
BC,
Canada
Matheron
G
(1963)
Principles
of
geostatistics.
Econ
Geol
58, 1246-1266
Matheron
G
(1971)
The
theory
of
regionalized

variables
and
its
applications.
Les
Cahiers
du
Centre
de
Mor-
phologie
Mathématique
de
Fontainebleau,
no
5,
ENSMP,
Paris,
France
McBratney
AB,
Webster
R
(1986)
Choosing
functions
for
semi-variograms
of
soil

properties
and
fitting
them
to
sampling
estimates.
J
Soil
Sci 37,
617-639
McCullagh
MJ
(1975)
Estimation
by
kriging
of
the
relia-
bility
of
the
proposed
trend
telemetry
network.
Com-
puter
Applications

2, 357-374
Nielsen
DR,
Biggar JW,
Erh
KT
(1973)
Spatial
variabil-
ity
of
field-measured
soil
water
properties.
Hilgardia
42, 215-260
Oliver
MA,
Webster
R
(1986)
Semi-variograms
for
mod-
elling
spatial
pattern
of
landform

and
soil
properties.
Earth
Surface
Processes
and
Landforms
11,
491-504
Palmer
MW
(1988)
Fractal
geometry:
a
tool
for
describ-
ing
spatial
patterns
of
plant
communities.
Vegetatio
75, 91-102
Pojar
J,
Klinka

K,
Meidinger
DV
(1987)
Biogeoclimatic
ecosystem
classification
in
British
Columbia.
For
Ecol
Manage
22, 119-154
Powers
RF
(1980)
Mineralizable
soil
nitrogen
as
an
index
of
nitrogen
availability
to
forest
trees.
Soil

Sci
Soc Amer J 44, 1314-1320
Robertson
GP
(1987)
Geostatistics
in
ecology:
interpo-
lating
with
known
variance.
Ecology 68,
744-748
Rossi
RE,
Mulla
DJ,
Journel
AG,
Franz
EH
(1992)
Geo-
statistical
tools
for
spatial
modelling

and
interpret-
ing
ecological
spatial
dependence.
Ecol Monogr 62,
277-314
Tabor
JA,
Warrick
AW,
Penningto
DA,
Myers
DE
(1984)
Spatial
variability
of
nitrate
in
irrigated
cotton.
I.
Peti-
oles.
Soil
Sci
Soc Amer J 48,

602-607
Trangmar
BB,
Yost
RS,
Uehara
G
(1985)
Application
of
geostatistics
to
spatial
studies
of
soil
properties.
In:
Advances
in
agronomy,
vol
38
(NC
Brady,
ed),
Aca-
demic
Press,
New

York,
NY,
USA,
45-94
Vauclin
M,
Vieira
SR,
Vachaud
G,
Nielsen
DR
(1983)
The
use
of
cokriging
with
limited
field
soil
observa-
tions.
Soil
Sci
Soc
Amer J 47,
175-184
Vieira
SR,

Nielsen
DR,
Biggar
JW
(1981)
Spatial
vari-
ability
of
field-measured
infiltration
rate.
Soil
Sci
Soc
Amer J 45, 1040-1048
Vieira
SR,
Hatfield
JL,
Nielsen
DR,
Biggar
JW
(1983)
Geostatistical
theory
and
application
to

variability
of
some
agronomical
properties.
Hilgardia 51,
1-75
Webster
R
(1985)
Quantiative
spatial
analysis
of
soil
in
the
field.
Adv
Soil
Sci
3,
1-70
Wilkinson
L
(1990a)
SYSTAT.
the
system
for statistics.

SYSTAT
Inc,
Evanston,
IL,
USA
Wilkinson
L
(1990b)
SYGRAPH:
the
system
for graphics.
SYSTAT
Inc,
Evanston,
IL,
USA
Xu
JY,
Webster
R
(1984)
A
geostatistical
study
of
topsoil
properties
in
Zhangwu

County,
China.
Catena
11,
13-26
Yost
RS,
Uehara
G,
Fox
RL
(1982a)
Geostatistical
anal-
ysis
of
soil
chemical
properties
of
large
land
areas.
I.
Semi-variograms.
Soil
Sci
Soc
Amer
J

46,
1028-
1032
Yost
RS,
Uehara
G,
Fox
RL
(1982b)
Geostatistical
anal-
ysis
of
soil
chemical
properties
of
large
land
areas.
II.
Kriging.
Soil
Sci
Soc
Amer
J
46,
1033-1037

Zar JH
(1984)
Biostatistical
analysis.
Prentice-Hall,
Engle-
wood
Cliffs,
NJ,
USA